The Cochran-Mantel-Haenszel (CMH) test is used to test multiple 2 × 2 contingency tables across different values of a confounding variable. The test determines whether there is a significant difference between the odds ratios across the different values of the confounding variable. Topics Basic Concepts Example Real Statistics Support References PennState (2017) Cochran-Mantel-Haenszel test https://online.stat.psu.edu/stat504/lesson/5/5.3/5.3.5 SAS … Read More
I am pleased to announce Release 5.3 of the Real Statistics Resource Pack. The new release is now available for free download at Download Resource Pack for Excel 2013 and 2016 (Windows version) environments. The resource pack for Excel 2007 and 2010 environments will be available later today or tomorrow. The resource pack for Excel 2011 and 2016 … Read More
I am proud to announce Release 5.1 of the Real Statistics Resource Pack, which is loaded with a lot of new features. The new release is now available for free download at Download Resource Pack for Excel 2013 and 2016 (Windows version) environments. The resource pack for Excel 2007 and 2010 environments will be available within the next … Read More
Worksheet Functions Real Statistics Functions: The Real Statistics Resource Pack contains the following array functions where R1 is an array containing an m × n contingency table, R2 is an mm × n array containing supplementary row profiles and R3 is an m × nn array containing supplementary column profiles. None of these arrays include row … Read More
Overview Correspondence analysis plays a role similar to factor analysis or principal component analysis for categorical data expressed as a contingency table (e.g. as described in the chi-square test of independence). For a 10 × 10, a complete description of the associations between row elements and column elements requires nine dimensions. Unfortunately, it is difficult … Read More
Correspondence analysis plays a role similar to factor analysis or principal component analysis for categorical data expressed as a contingency table (e.g. as described in the chi-square test of independence). Essentially, correspondence analysis decomposes the chi-square statistic of independence into orthogonal factors. This approach is valid even when the cell sizes in the contingency table … Read More
Worksheet Functions Real Statistics Functions: The Real Statistics Pack provides the following worksheet functions: TCORREL(R1, lab, opt, alpha): outputs a column array containing the tetrachoric correlation coefficient for the 2 × 2 contingency table in range R1 (without headings), standard error, z statistic, p-value, and the lower and upper limits of the 1 – alpha … Read More
We now describe how to estimate the tetrachoric correlation coefficient, i.e. the polychoric correlation coefficient for 2 × 2 contingency tables. In what follows we assume that the contingency table has 2 rows and 2 columns where the element in the ith row and jth column is aij. Method 1 An estimate for the tetrachoric … Read More
Objective Suppose we have a contingency table with m rows and n columns. Further, suppose that the element in the ith row and jth column is aij. Our goal now is to find the value of ρ which maximizes the log-likelihood function LL where We can accomplish this by using Excel’s Solver. Example Example 1: Calculate … Read More
Introduction When data is organized in the form of a contingency table (see Independence Testing) where the two categorical independent variables (corresponding to the row and columns) are ordered, then we can calculate a polychoric correlation coefficient. This coefficient is an approximation to what Pearson’s correlation coefficient would be if we had continuous data. For … Read More